Geodesic
First-order partial differential equations with large high-frequency terms
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 11, pp. 2024-2041

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Systems of first-order semilinear partial differential equations with terms that oscillate at a frequency $\omega\gg1$ in a single variable and are proportional to $\sqrt\omega$ are considered. The Krylov–Bogolyubov–Mitropol'skii averaging method is substantiated for such equations. Based on the two-scale expansion method, an algorithm for constructing complete asymptotics of solutions is proposed and justified. 
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     author = {A. K. Kapikyan and V. B. Levenshtam},
     title = {First-order partial differential equations with large high-frequency terms},
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A. K. Kapikyan; V. B. Levenshtam. First-order partial differential equations with large high-frequency terms. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 11, pp. 2024-2041. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_11_a10/